I think it would be very useful to assign users into departments.
Tickets could then be assigned to a department, and someone within that department could then take the ticket and work on it.

This would be great where you don't know which of Bob or Alice is likly to want to be assigned the ticket. You can just give it to their dept, and let their manager sort it out.
As opposed to the current case, where you have to know who to assign a ticket too, which means knowing a lot about the workloads of everyone in the company